Summary: Compact Representation of Multidimensional Data Using Tensor Rank­One
Decomposition
Hongcheng Wang, Narendra Ahuja
Beckman Institute, University of Illinois at Urbana­Champaign, USA
{wanghc,ahuja }@vision.ai.uiuc.edu
Abstract
This paper presents a new approach for representing
multidimensional data by a compact number of bases. We
consider the multidimensional data as tensors instead of
matrices or vectors, and propose a Tensor Rank­One De­
composition (TROD) algorithm by decomposing Nth­order
data into a collection of rank­1 tensors based on multilin­
ear algebra. By applying this algorithm to image sequence
compression, we obtain much higher quality images with
the same compression ratio as Principle Component Analy­
sis (PCA). Experiments with gray­level and color video se­
quences are used to illustrate the validity of this approach.
1. Introduction
In computer vision and graphics, we often encounter
multidimensional data, such as images, video, range data